Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(47.9341963334\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 13 x^{10} + 41 x^{9} + 54 x^{8} - 188 x^{7} - 77 x^{6} + 342 x^{5} + 13 x^{4} - 215 x^{3} + 9 x^{2} + 37 x - 5 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 667) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Root | \(2.66955\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.66955 | 1.88765 | 0.943827 | − | 0.330440i | \(-0.107197\pi\) | ||||
0.943827 | + | 0.330440i | \(0.107197\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.12647 | 2.56324 | ||||||||
\(5\) | 2.89555 | 1.29493 | 0.647466 | − | 0.762095i | \(-0.275829\pi\) | ||||
0.647466 | + | 0.762095i | \(0.275829\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.268248 | −0.101388 | −0.0506940 | − | 0.998714i | \(-0.516143\pi\) | ||||
−0.0506940 | + | 0.998714i | \(0.516143\pi\) | |||||||
\(8\) | 8.34627 | 2.95085 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 7.72982 | 2.44438 | ||||||||
\(11\) | −5.35238 | −1.61380 | −0.806902 | − | 0.590685i | \(-0.798857\pi\) | ||||
−0.806902 | + | 0.590685i | \(0.798857\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.85670 | 1.06966 | 0.534828 | − | 0.844961i | \(-0.320376\pi\) | ||||
0.534828 | + | 0.844961i | \(0.320376\pi\) | |||||||
\(14\) | −0.716099 | −0.191386 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.0278 | 3.00695 | ||||||||
\(17\) | 3.41249 | 0.827650 | 0.413825 | − | 0.910356i | \(-0.364192\pi\) | ||||
0.413825 | + | 0.910356i | \(0.364192\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.28684 | −0.983468 | −0.491734 | − | 0.870746i | \(-0.663637\pi\) | ||||
−0.491734 | + | 0.870746i | \(0.663637\pi\) | |||||||
\(20\) | 14.8440 | 3.31922 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −14.2884 | −3.04630 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.38424 | 0.676848 | ||||||||
\(26\) | 10.2956 | 2.01914 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.37516 | −0.259882 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.06011 | 0.549612 | 0.274806 | − | 0.961500i | \(-0.411386\pi\) | ||||
0.274806 | + | 0.961500i | \(0.411386\pi\) | |||||||
\(32\) | 15.4162 | 2.72523 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.10980 | 1.56232 | ||||||||
\(35\) | −0.776726 | −0.131291 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65787 | 0.930147 | 0.465074 | − | 0.885272i | \(-0.346028\pi\) | ||||
0.465074 | + | 0.885272i | \(0.346028\pi\) | |||||||
\(38\) | −11.4439 | −1.85645 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 24.1671 | 3.82115 | ||||||||
\(41\) | 2.62648 | 0.410188 | 0.205094 | − | 0.978742i | \(-0.434250\pi\) | ||||
0.205094 | + | 0.978742i | \(0.434250\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.20369 | −0.946054 | −0.473027 | − | 0.881048i | \(-0.656839\pi\) | ||||
−0.473027 | + | 0.881048i | \(0.656839\pi\) | |||||||
\(44\) | −27.4389 | −4.13656 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.66955 | 0.393603 | ||||||||
\(47\) | 12.2344 | 1.78456 | 0.892282 | − | 0.451478i | \(-0.149103\pi\) | ||||
0.892282 | + | 0.451478i | \(0.149103\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92804 | −0.989720 | ||||||||
\(50\) | 9.03438 | 1.27765 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.7713 | 2.74178 | ||||||||
\(53\) | 12.5555 | 1.72463 | 0.862316 | − | 0.506371i | \(-0.169013\pi\) | ||||
0.862316 | + | 0.506371i | \(0.169013\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.4981 | −2.08977 | ||||||||
\(56\) | −2.23887 | −0.299181 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.66955 | 0.350529 | ||||||||
\(59\) | −9.30093 | −1.21088 | −0.605439 | − | 0.795892i | \(-0.707002\pi\) | ||||
−0.605439 | + | 0.795892i | \(0.707002\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.39308 | 1.20266 | 0.601330 | − | 0.799001i | \(-0.294638\pi\) | ||||
0.601330 | + | 0.799001i | \(0.294638\pi\) | |||||||
\(62\) | 8.16910 | 1.03748 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 17.0987 | 2.13734 | ||||||||
\(65\) | 11.1673 | 1.38513 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.45335 | −0.666233 | −0.333117 | − | 0.942886i | \(-0.608100\pi\) | ||||
−0.333117 | + | 0.942886i | \(0.608100\pi\) | |||||||
\(68\) | 17.4940 | 2.12146 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.07350 | −0.247831 | ||||||||
\(71\) | 14.0578 | 1.66835 | 0.834175 | − | 0.551500i | \(-0.185944\pi\) | ||||
0.834175 | + | 0.551500i | \(0.185944\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.27709 | −0.734677 | −0.367339 | − | 0.930087i | \(-0.619731\pi\) | ||||
−0.367339 | + | 0.930087i | \(0.619731\pi\) | |||||||
\(74\) | 15.1039 | 1.75580 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −21.9764 | −2.52086 | ||||||||
\(77\) | 1.43576 | 0.163620 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.39080 | −1.05655 | −0.528274 | − | 0.849074i | \(-0.677160\pi\) | ||||
−0.528274 | + | 0.849074i | \(0.677160\pi\) | |||||||
\(80\) | 34.8271 | 3.89379 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.01152 | 0.774293 | ||||||||
\(83\) | −4.93812 | −0.542029 | −0.271014 | − | 0.962575i | \(-0.587359\pi\) | ||||
−0.271014 | + | 0.962575i | \(0.587359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.88105 | 1.07175 | ||||||||
\(86\) | −16.5610 | −1.78582 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −44.6724 | −4.76209 | ||||||||
\(89\) | −6.26188 | −0.663758 | −0.331879 | − | 0.943322i | \(-0.607683\pi\) | ||||
−0.331879 | + | 0.943322i | \(0.607683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.03455 | −0.108450 | ||||||||
\(92\) | 5.12647 | 0.534472 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 32.6602 | 3.36864 | ||||||||
\(95\) | −12.4128 | −1.27352 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.54652 | −0.360094 | −0.180047 | − | 0.983658i | \(-0.557625\pi\) | ||||
−0.180047 | + | 0.983658i | \(0.557625\pi\) | |||||||
\(98\) | −18.4947 | −1.86825 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 17.3492 | 1.73492 | ||||||||
\(101\) | −1.47360 | −0.146629 | −0.0733143 | − | 0.997309i | \(-0.523358\pi\) | ||||
−0.0733143 | + | 0.997309i | \(0.523358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0201 | −1.57851 | −0.789256 | − | 0.614065i | \(-0.789533\pi\) | ||||
−0.789256 | + | 0.614065i | \(0.789533\pi\) | |||||||
\(104\) | 32.1890 | 3.15639 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 33.5175 | 3.25551 | ||||||||
\(107\) | 16.6653 | 1.61109 | 0.805546 | − | 0.592534i | \(-0.201872\pi\) | ||||
0.805546 | + | 0.592534i | \(0.201872\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.9091 | −1.33225 | −0.666124 | − | 0.745841i | \(-0.732048\pi\) | ||||
−0.666124 | + | 0.745841i | \(0.732048\pi\) | |||||||
\(110\) | −41.3729 | −3.94475 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.22643 | −0.304869 | ||||||||
\(113\) | 0.244699 | 0.0230193 | 0.0115096 | − | 0.999934i | \(-0.496336\pi\) | ||||
0.0115096 | + | 0.999934i | \(0.496336\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.89555 | 0.270012 | ||||||||
\(116\) | 5.12647 | 0.475981 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −24.8293 | −2.28572 | ||||||||
\(119\) | −0.915392 | −0.0839139 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.6480 | 1.60436 | ||||||||
\(122\) | 25.0753 | 2.27021 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.6876 | 1.40879 | ||||||||
\(125\) | −4.67853 | −0.418460 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.70418 | 0.151221 | 0.0756107 | − | 0.997137i | \(-0.475909\pi\) | ||||
0.0756107 | + | 0.997137i | \(0.475909\pi\) | |||||||
\(128\) | 14.8133 | 1.30932 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 29.8116 | 2.61465 | ||||||||
\(131\) | −10.1176 | −0.883976 | −0.441988 | − | 0.897021i | \(-0.645727\pi\) | ||||
−0.441988 | + | 0.897021i | \(0.645727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14993 | 0.0997119 | ||||||||
\(134\) | −14.5580 | −1.25762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.4816 | 2.44227 | ||||||||
\(137\) | −2.99872 | −0.256198 | −0.128099 | − | 0.991761i | \(-0.540888\pi\) | ||||
−0.128099 | + | 0.991761i | \(0.540888\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.8537 | −1.00541 | −0.502707 | − | 0.864457i | \(-0.667662\pi\) | ||||
−0.502707 | + | 0.864457i | \(0.667662\pi\) | |||||||
\(140\) | −3.98186 | −0.336529 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 37.5278 | 3.14927 | ||||||||
\(143\) | −20.6425 | −1.72621 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.89555 | 0.240463 | ||||||||
\(146\) | −16.7570 | −1.38682 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 29.0049 | 2.38419 | ||||||||
\(149\) | 1.41163 | 0.115645 | 0.0578227 | − | 0.998327i | \(-0.481584\pi\) | ||||
0.0578227 | + | 0.998327i | \(0.481584\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.16319 | 0.338795 | 0.169398 | − | 0.985548i | \(-0.445818\pi\) | ||||
0.169398 | + | 0.985548i | \(0.445818\pi\) | |||||||
\(152\) | −35.7791 | −2.90207 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.83284 | 0.308859 | ||||||||
\(155\) | 8.86071 | 0.711710 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.8086 | −1.42128 | −0.710641 | − | 0.703555i | \(-0.751595\pi\) | ||||
−0.710641 | + | 0.703555i | \(0.751595\pi\) | |||||||
\(158\) | −25.0692 | −1.99440 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 44.6385 | 3.52898 | ||||||||
\(161\) | −0.268248 | −0.0211409 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3775 | 0.969482 | 0.484741 | − | 0.874658i | \(-0.338914\pi\) | ||||
0.484741 | + | 0.874658i | \(0.338914\pi\) | |||||||
\(164\) | 13.4646 | 1.05141 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1825 | −1.02316 | ||||||||
\(167\) | 6.88064 | 0.532440 | 0.266220 | − | 0.963912i | \(-0.414225\pi\) | ||||
0.266220 | + | 0.963912i | \(0.414225\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.87412 | 0.144163 | ||||||||
\(170\) | 26.3779 | 2.02309 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −31.8031 | −2.42496 | ||||||||
\(173\) | 6.22503 | 0.473280 | 0.236640 | − | 0.971597i | \(-0.423954\pi\) | ||||
0.236640 | + | 0.971597i | \(0.423954\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.907814 | −0.0686243 | ||||||||
\(176\) | −64.3773 | −4.85262 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.7164 | −1.25295 | ||||||||
\(179\) | −22.4493 | −1.67794 | −0.838969 | − | 0.544179i | \(-0.816841\pi\) | ||||
−0.838969 | + | 0.544179i | \(0.816841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.29095 | −0.318944 | −0.159472 | − | 0.987202i | \(-0.550979\pi\) | ||||
−0.159472 | + | 0.987202i | \(0.550979\pi\) | |||||||
\(182\) | −2.76178 | −0.204717 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.34627 | 0.615295 | ||||||||
\(185\) | 16.3827 | 1.20448 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −18.2649 | −1.33567 | ||||||||
\(188\) | 62.7191 | 4.57426 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −33.1365 | −2.40397 | ||||||||
\(191\) | −16.7358 | −1.21096 | −0.605479 | − | 0.795861i | \(-0.707018\pi\) | ||||
−0.605479 | + | 0.795861i | \(0.707018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.2950 | 1.17294 | 0.586468 | − | 0.809972i | \(-0.300518\pi\) | ||||
0.586468 | + | 0.809972i | \(0.300518\pi\) | |||||||
\(194\) | −9.46759 | −0.679733 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −35.5164 | −2.53689 | ||||||||
\(197\) | −20.6304 | −1.46986 | −0.734928 | − | 0.678145i | \(-0.762784\pi\) | ||||
−0.734928 | + | 0.678145i | \(0.762784\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8346 | −0.909822 | −0.454911 | − | 0.890537i | \(-0.650329\pi\) | ||||
−0.454911 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(200\) | 28.2458 | 1.99728 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.93384 | −0.276784 | ||||||||
\(203\) | −0.268248 | −0.0188273 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.60513 | 0.531165 | ||||||||
\(206\) | −42.7665 | −2.97968 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 46.3876 | 3.21640 | ||||||||
\(209\) | 22.9448 | 1.58712 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.39689 | 0.646908 | 0.323454 | − | 0.946244i | \(-0.395156\pi\) | ||||
0.323454 | + | 0.946244i | \(0.395156\pi\) | |||||||
\(212\) | 64.3655 | 4.42064 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 44.4887 | 3.04118 | ||||||||
\(215\) | −17.9631 | −1.22507 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.820867 | −0.0557241 | ||||||||
\(218\) | −37.1309 | −2.51482 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −79.4507 | −5.35656 | ||||||||
\(221\) | 13.1609 | 0.885301 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.7757 | −1.45821 | −0.729104 | − | 0.684403i | \(-0.760063\pi\) | ||||
−0.729104 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(224\) | −4.13536 | −0.276305 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.653234 | 0.0434525 | ||||||||
\(227\) | −10.6634 | −0.707756 | −0.353878 | − | 0.935292i | \(-0.615137\pi\) | ||||
−0.353878 | + | 0.935292i | \(0.615137\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.68682 | 0.640123 | 0.320062 | − | 0.947397i | \(-0.396296\pi\) | ||||
0.320062 | + | 0.947397i | \(0.396296\pi\) | |||||||
\(230\) | 7.72982 | 0.509689 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.34627 | 0.547959 | ||||||||
\(233\) | −17.9188 | −1.17390 | −0.586949 | − | 0.809624i | \(-0.699671\pi\) | ||||
−0.586949 | + | 0.809624i | \(0.699671\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 35.4253 | 2.31089 | ||||||||
\(236\) | −47.6810 | −3.10377 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.44368 | −0.158400 | ||||||||
\(239\) | 1.53321 | 0.0991752 | 0.0495876 | − | 0.998770i | \(-0.484209\pi\) | ||||
0.0495876 | + | 0.998770i | \(0.484209\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.97835 | 0.385099 | 0.192550 | − | 0.981287i | \(-0.438324\pi\) | ||||
0.192550 | + | 0.981287i | \(0.438324\pi\) | |||||||
\(242\) | 47.1121 | 3.02848 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 48.1534 | 3.08270 | ||||||||
\(245\) | −20.0605 | −1.28162 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −16.5330 | −1.05197 | ||||||||
\(248\) | 25.5405 | 1.62182 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.4895 | −0.789908 | ||||||||
\(251\) | −6.57893 | −0.415258 | −0.207629 | − | 0.978208i | \(-0.566575\pi\) | ||||
−0.207629 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.35238 | −0.336501 | ||||||||
\(254\) | 4.54938 | 0.285454 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5.34744 | 0.334215 | ||||||||
\(257\) | −2.86807 | −0.178905 | −0.0894527 | − | 0.995991i | \(-0.528512\pi\) | ||||
−0.0894527 | + | 0.995991i | \(0.528512\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.51771 | −0.0943058 | ||||||||
\(260\) | 57.2488 | 3.55042 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −27.0093 | −1.66864 | ||||||||
\(263\) | −16.9954 | −1.04798 | −0.523991 | − | 0.851724i | \(-0.675558\pi\) | ||||
−0.523991 | + | 0.851724i | \(0.675558\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 36.3552 | 2.23328 | ||||||||
\(266\) | 3.06980 | 0.188222 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −27.9565 | −1.70771 | ||||||||
\(269\) | 20.5857 | 1.25514 | 0.627568 | − | 0.778562i | \(-0.284051\pi\) | ||||
0.627568 | + | 0.778562i | \(0.284051\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.1461 | 1.58826 | 0.794130 | − | 0.607747i | \(-0.207927\pi\) | ||||
0.794130 | + | 0.607747i | \(0.207927\pi\) | |||||||
\(272\) | 41.0447 | 2.48870 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.00522 | −0.483613 | ||||||||
\(275\) | −18.1137 | −1.09230 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.31984 | −0.319638 | −0.159819 | − | 0.987146i | \(-0.551091\pi\) | ||||
−0.159819 | + | 0.987146i | \(0.551091\pi\) | |||||||
\(278\) | −31.6439 | −1.89787 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −6.48276 | −0.387419 | ||||||||
\(281\) | 10.8523 | 0.647396 | 0.323698 | − | 0.946160i | \(-0.395074\pi\) | ||||
0.323698 | + | 0.946160i | \(0.395074\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.31750 | −0.375536 | −0.187768 | − | 0.982213i | \(-0.560125\pi\) | ||||
−0.187768 | + | 0.982213i | \(0.560125\pi\) | |||||||
\(284\) | 72.0668 | 4.27637 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −55.1062 | −3.25850 | ||||||||
\(287\) | −0.704548 | −0.0415881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.35491 | −0.314995 | ||||||||
\(290\) | 7.72982 | 0.453910 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −32.1793 | −1.88315 | ||||||||
\(293\) | 3.14022 | 0.183454 | 0.0917268 | − | 0.995784i | \(-0.470761\pi\) | ||||
0.0917268 | + | 0.995784i | \(0.470761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −26.9313 | −1.56800 | ||||||||
\(296\) | 47.2221 | 2.74473 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.76842 | 0.218298 | ||||||||
\(299\) | 3.85670 | 0.223039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.66412 | 0.0959185 | ||||||||
\(302\) | 11.1138 | 0.639528 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −51.5612 | −2.95724 | ||||||||
\(305\) | 27.1982 | 1.55736 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.7708 | 1.12838 | 0.564191 | − | 0.825644i | \(-0.309188\pi\) | ||||
0.564191 | + | 0.825644i | \(0.309188\pi\) | |||||||
\(308\) | 7.36040 | 0.419398 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.6541 | 1.34346 | ||||||||
\(311\) | 15.9208 | 0.902788 | 0.451394 | − | 0.892325i | \(-0.350927\pi\) | ||||
0.451394 | + | 0.892325i | \(0.350927\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.2341 | −1.82198 | −0.910991 | − | 0.412427i | \(-0.864681\pi\) | ||||
−0.910991 | + | 0.412427i | \(0.864681\pi\) | |||||||
\(314\) | −47.5409 | −2.68289 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −48.1417 | −2.70818 | ||||||||
\(317\) | 4.03526 | 0.226643 | 0.113321 | − | 0.993558i | \(-0.463851\pi\) | ||||
0.113321 | + | 0.993558i | \(0.463851\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.35238 | −0.299676 | ||||||||
\(320\) | 49.5102 | 2.76770 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.716099 | −0.0399066 | ||||||||
\(323\) | −14.6288 | −0.813967 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 13.0520 | 0.723994 | ||||||||
\(326\) | 33.0423 | 1.83005 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 21.9213 | 1.21040 | ||||||||
\(329\) | −3.28184 | −0.180934 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2270 | 0.946880 | 0.473440 | − | 0.880826i | \(-0.343012\pi\) | ||||
0.473440 | + | 0.880826i | \(0.343012\pi\) | |||||||
\(332\) | −25.3151 | −1.38935 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.3682 | 1.00506 | ||||||||
\(335\) | −15.7905 | −0.862726 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.67028 | −0.308880 | −0.154440 | − | 0.988002i | \(-0.549357\pi\) | ||||
−0.154440 | + | 0.988002i | \(0.549357\pi\) | |||||||
\(338\) | 5.00305 | 0.272130 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 50.6550 | 2.74715 | ||||||||
\(341\) | −16.3789 | −0.886966 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.73616 | 0.201734 | ||||||||
\(344\) | −51.7776 | −2.79166 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.6180 | 0.893390 | ||||||||
\(347\) | −11.3415 | −0.608843 | −0.304422 | − | 0.952537i | \(-0.598463\pi\) | ||||
−0.304422 | + | 0.952537i | \(0.598463\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.3888 | −1.62668 | −0.813338 | − | 0.581792i | \(-0.802352\pi\) | ||||
−0.813338 | + | 0.581792i | \(0.802352\pi\) | |||||||
\(350\) | −2.42345 | −0.129539 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −82.5134 | −4.39798 | ||||||||
\(353\) | −32.2636 | −1.71722 | −0.858609 | − | 0.512631i | \(-0.828671\pi\) | ||||
−0.858609 | + | 0.512631i | \(0.828671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 40.7050 | 2.16040 | ||||||||
\(356\) | −32.1014 | −1.70137 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −59.9294 | −3.16737 | ||||||||
\(359\) | −2.03999 | −0.107667 | −0.0538333 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538333 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.623032 | −0.0327911 | ||||||||
\(362\) | −11.4549 | −0.602056 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.30359 | −0.277984 | ||||||||
\(365\) | −18.1756 | −0.951357 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −25.1042 | −1.31043 | −0.655214 | − | 0.755443i | \(-0.727422\pi\) | ||||
−0.655214 | + | 0.755443i | \(0.727422\pi\) | |||||||
\(368\) | 12.0278 | 0.626992 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 43.7343 | 2.27364 | ||||||||
\(371\) | −3.36799 | −0.174857 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.9976 | 1.19077 | 0.595386 | − | 0.803439i | \(-0.296999\pi\) | ||||
0.595386 | + | 0.803439i | \(0.296999\pi\) | |||||||
\(374\) | −48.7591 | −2.52127 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 102.111 | 5.26598 | ||||||||
\(377\) | 3.85670 | 0.198630 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.9225 | 1.53702 | 0.768509 | − | 0.639839i | \(-0.220999\pi\) | ||||
0.768509 | + | 0.639839i | \(0.220999\pi\) | |||||||
\(380\) | −63.6338 | −3.26434 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −44.6769 | −2.28587 | ||||||||
\(383\) | 21.5495 | 1.10113 | 0.550563 | − | 0.834793i | \(-0.314413\pi\) | ||||
0.550563 | + | 0.834793i | \(0.314413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.15733 | 0.211877 | ||||||||
\(386\) | 43.5001 | 2.21410 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.1811 | −0.923007 | ||||||||
\(389\) | 18.0550 | 0.915424 | 0.457712 | − | 0.889101i | \(-0.348669\pi\) | ||||
0.457712 | + | 0.889101i | \(0.348669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.41249 | 0.172577 | ||||||||
\(392\) | −57.8233 | −2.92052 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −55.0738 | −2.77458 | ||||||||
\(395\) | −27.1916 | −1.36816 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.421308 | −0.0211449 | −0.0105724 | − | 0.999944i | \(-0.503365\pi\) | ||||
−0.0105724 | + | 0.999944i | \(0.503365\pi\) | |||||||
\(398\) | −34.2626 | −1.71743 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 40.7049 | 2.03525 | ||||||||
\(401\) | 30.3737 | 1.51679 | 0.758394 | − | 0.651796i | \(-0.225984\pi\) | ||||
0.758394 | + | 0.651796i | \(0.225984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8019 | 0.587895 | ||||||||
\(404\) | −7.55437 | −0.375844 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.716099 | −0.0355394 | ||||||||
\(407\) | −30.2831 | −1.50108 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.5636 | 1.16514 | 0.582572 | − | 0.812779i | \(-0.302046\pi\) | ||||
0.582572 | + | 0.812779i | \(0.302046\pi\) | |||||||
\(410\) | 20.3022 | 1.00266 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −82.1269 | −4.04610 | ||||||||
\(413\) | 2.49495 | 0.122769 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2986 | −0.701890 | ||||||||
\(416\) | 59.4557 | 2.91505 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 61.2522 | 2.99594 | ||||||||
\(419\) | 31.9090 | 1.55885 | 0.779427 | − | 0.626493i | \(-0.215510\pi\) | ||||
0.779427 | + | 0.626493i | \(0.215510\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.6752 | −0.958911 | −0.479456 | − | 0.877566i | \(-0.659166\pi\) | ||||
−0.479456 | + | 0.877566i | \(0.659166\pi\) | |||||||
\(422\) | 25.0854 | 1.22114 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 104.792 | 5.08913 | ||||||||
\(425\) | 11.5487 | 0.560193 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.51967 | −0.121935 | ||||||||
\(428\) | 85.4340 | 4.12961 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −47.9534 | −2.31252 | ||||||||
\(431\) | −34.6117 | −1.66719 | −0.833594 | − | 0.552378i | \(-0.813720\pi\) | ||||
−0.833594 | + | 0.552378i | \(0.813720\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.3428 | 1.31401 | 0.657006 | − | 0.753885i | \(-0.271823\pi\) | ||||
0.657006 | + | 0.753885i | \(0.271823\pi\) | |||||||
\(434\) | −2.19134 | −0.105188 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.3045 | −3.41487 | ||||||||
\(437\) | −4.28684 | −0.205067 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.0183 | 1.24178 | 0.620892 | − | 0.783896i | \(-0.286771\pi\) | ||||
0.620892 | + | 0.783896i | \(0.286771\pi\) | |||||||
\(440\) | −129.351 | −6.16659 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 35.1337 | 1.67114 | ||||||||
\(443\) | 7.52187 | 0.357375 | 0.178687 | − | 0.983906i | \(-0.442815\pi\) | ||||
0.178687 | + | 0.983906i | \(0.442815\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.1316 | −0.859521 | ||||||||
\(446\) | −58.1312 | −2.75259 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.58668 | −0.216700 | ||||||||
\(449\) | −41.2802 | −1.94813 | −0.974067 | − | 0.226261i | \(-0.927350\pi\) | ||||
−0.974067 | + | 0.226261i | \(0.927350\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0579 | −0.661963 | ||||||||
\(452\) | 1.25444 | 0.0590039 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −28.4665 | −1.33600 | ||||||||
\(455\) | −2.99560 | −0.140436 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.9955 | 0.888572 | 0.444286 | − | 0.895885i | \(-0.353457\pi\) | ||||
0.444286 | + | 0.895885i | \(0.353457\pi\) | |||||||
\(458\) | 25.8594 | 1.20833 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.8440 | 0.692105 | ||||||||
\(461\) | 23.7949 | 1.10824 | 0.554119 | − | 0.832437i | \(-0.313055\pi\) | ||||
0.554119 | + | 0.832437i | \(0.313055\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.43032 | −0.112947 | −0.0564733 | − | 0.998404i | \(-0.517986\pi\) | ||||
−0.0564733 | + | 0.998404i | \(0.517986\pi\) | |||||||
\(464\) | 12.0278 | 0.558376 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −47.8350 | −2.21591 | ||||||||
\(467\) | 6.85798 | 0.317350 | 0.158675 | − | 0.987331i | \(-0.449278\pi\) | ||||
0.158675 | + | 0.987331i | \(0.449278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.46285 | 0.0675481 | ||||||||
\(470\) | 94.5693 | 4.36216 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −77.6280 | −3.57312 | ||||||||
\(473\) | 33.2045 | 1.52675 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.5077 | −0.665658 | ||||||||
\(476\) | −4.69273 | −0.215091 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.09298 | 0.187208 | ||||||||
\(479\) | −16.3926 | −0.748999 | −0.374500 | − | 0.927227i | \(-0.622186\pi\) | ||||
−0.374500 | + | 0.927227i | \(0.622186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.8207 | 0.994937 | ||||||||
\(482\) | 15.9595 | 0.726934 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 90.4720 | 4.11236 | ||||||||
\(485\) | −10.2691 | −0.466297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.4676 | −1.42594 | −0.712968 | − | 0.701197i | \(-0.752649\pi\) | ||||
−0.712968 | + | 0.701197i | \(0.752649\pi\) | |||||||
\(488\) | 78.3971 | 3.54887 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −53.5525 | −2.41926 | ||||||||
\(491\) | 34.0891 | 1.53842 | 0.769209 | − | 0.638997i | \(-0.220650\pi\) | ||||
0.769209 | + | 0.638997i | \(0.220650\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.41249 | 0.153691 | ||||||||
\(494\) | −44.1357 | −1.98576 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 36.8064 | 1.65265 | ||||||||
\(497\) | −3.77096 | −0.169151 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.1962 | 1.03840 | 0.519201 | − | 0.854652i | \(-0.326229\pi\) | ||||
0.519201 | + | 0.854652i | \(0.326229\pi\) | |||||||
\(500\) | −23.9844 | −1.07261 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −17.5628 | −0.783864 | ||||||||
\(503\) | 26.0785 | 1.16278 | 0.581391 | − | 0.813624i | \(-0.302509\pi\) | ||||
0.581391 | + | 0.813624i | \(0.302509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.26689 | −0.189874 | ||||||||
\(506\) | −14.2884 | −0.635198 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.73643 | 0.387616 | ||||||||
\(509\) | 39.1346 | 1.73461 | 0.867305 | − | 0.497777i | \(-0.165850\pi\) | ||||
0.867305 | + | 0.497777i | \(0.165850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.68381 | 0.0744875 | ||||||||
\(512\) | −15.3514 | −0.678442 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.65645 | −0.337711 | ||||||||
\(515\) | −46.3872 | −2.04406 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −65.4830 | −2.87994 | ||||||||
\(518\) | −4.05159 | −0.178017 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 93.2051 | 4.08731 | ||||||||
\(521\) | 12.7309 | 0.557753 | 0.278876 | − | 0.960327i | \(-0.410038\pi\) | ||||
0.278876 | + | 0.960327i | \(0.410038\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.4547 | −1.28796 | −0.643982 | − | 0.765041i | \(-0.722719\pi\) | ||||
−0.643982 | + | 0.765041i | \(0.722719\pi\) | |||||||
\(524\) | −51.8674 | −2.26584 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −45.3700 | −1.97823 | ||||||||
\(527\) | 10.4426 | 0.454886 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 97.0518 | 4.21566 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.89510 | 0.255585 | ||||||||
\(533\) | 10.1296 | 0.438760 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 48.2552 | 2.08625 | ||||||||
\(536\) | −45.5151 | −1.96595 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 54.9546 | 2.36926 | ||||||||
\(539\) | 37.0815 | 1.59721 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.8062 | −1.02351 | −0.511754 | − | 0.859132i | \(-0.671004\pi\) | ||||
−0.511754 | + | 0.859132i | \(0.671004\pi\) | |||||||
\(542\) | 69.7981 | 2.99809 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 52.6077 | 2.25553 | ||||||||
\(545\) | −40.2745 | −1.72517 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.3531 | 0.613695 | 0.306847 | − | 0.951759i | \(-0.400726\pi\) | ||||
0.306847 | + | 0.951759i | \(0.400726\pi\) | |||||||
\(548\) | −15.3729 | −0.656696 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −48.3554 | −2.06188 | ||||||||
\(551\) | −4.28684 | −0.182625 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.51906 | 0.107121 | ||||||||
\(554\) | −14.2016 | −0.603367 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −60.7674 | −2.57711 | ||||||||
\(557\) | −18.3031 | −0.775528 | −0.387764 | − | 0.921759i | \(-0.626752\pi\) | ||||
−0.387764 | + | 0.921759i | \(0.626752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.9258 | −1.01195 | ||||||||
\(560\) | −9.34229 | −0.394784 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.9708 | 1.22206 | ||||||||
\(563\) | −4.64703 | −0.195849 | −0.0979245 | − | 0.995194i | \(-0.531220\pi\) | ||||
−0.0979245 | + | 0.995194i | \(0.531220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.708538 | 0.0298084 | ||||||||
\(566\) | −16.8649 | −0.708883 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 117.330 | 4.92305 | ||||||||
\(569\) | 36.6541 | 1.53662 | 0.768309 | − | 0.640079i | \(-0.221098\pi\) | ||||
0.768309 | + | 0.640079i | \(0.221098\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.18890 | −0.217149 | −0.108574 | − | 0.994088i | \(-0.534629\pi\) | ||||
−0.108574 | + | 0.994088i | \(0.534629\pi\) | |||||||
\(572\) | −105.823 | −4.42470 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.88082 | −0.0785040 | ||||||||
\(575\) | 3.38424 | 0.141132 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.5672 | 0.439920 | 0.219960 | − | 0.975509i | \(-0.429407\pi\) | ||||
0.219960 | + | 0.975509i | \(0.429407\pi\) | |||||||
\(578\) | −14.2952 | −0.594601 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14.8440 | 0.616363 | ||||||||
\(581\) | 1.32464 | 0.0549552 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −67.2019 | −2.78322 | ||||||||
\(584\) | −52.3902 | −2.16792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.38296 | 0.346297 | ||||||||
\(587\) | 6.64788 | 0.274387 | 0.137194 | − | 0.990544i | \(-0.456192\pi\) | ||||
0.137194 | + | 0.990544i | \(0.456192\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.1182 | −0.540526 | ||||||||
\(590\) | −71.8945 | −2.95985 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 68.0516 | 2.79690 | ||||||||
\(593\) | 31.3241 | 1.28633 | 0.643164 | − | 0.765729i | \(-0.277622\pi\) | ||||
0.643164 | + | 0.765729i | \(0.277622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.65057 | −0.108663 | ||||||||
\(596\) | 7.23669 | 0.296427 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.2956 | 0.421020 | ||||||||
\(599\) | −19.9482 | −0.815059 | −0.407530 | − | 0.913192i | \(-0.633610\pi\) | ||||
−0.407530 | + | 0.913192i | \(0.633610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.9631 | −0.691940 | −0.345970 | − | 0.938246i | \(-0.612450\pi\) | ||||
−0.345970 | + | 0.938246i | \(0.612450\pi\) | |||||||
\(602\) | 4.44246 | 0.181061 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.3425 | 0.868413 | ||||||||
\(605\) | 51.1007 | 2.07754 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.19316 | −0.170195 | −0.0850975 | − | 0.996373i | \(-0.527120\pi\) | ||||
−0.0850975 | + | 0.996373i | \(0.527120\pi\) | |||||||
\(608\) | −66.0868 | −2.68017 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 72.6068 | 2.93976 | ||||||||
\(611\) | 47.1842 | 1.90887 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.0079 | 1.17162 | 0.585809 | − | 0.810449i | \(-0.300777\pi\) | ||||
0.585809 | + | 0.810449i | \(0.300777\pi\) | |||||||
\(614\) | 52.7792 | 2.12999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.9833 | 0.482820 | ||||||||
\(617\) | 32.8667 | 1.32316 | 0.661581 | − | 0.749874i | \(-0.269886\pi\) | ||||
0.661581 | + | 0.749874i | \(0.269886\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.2241 | −0.451137 | −0.225568 | − | 0.974227i | \(-0.572424\pi\) | ||||
−0.225568 | + | 0.974227i | \(0.572424\pi\) | |||||||
\(620\) | 45.4242 | 1.82428 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 42.5014 | 1.70415 | ||||||||
\(623\) | 1.67973 | 0.0672972 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4681 | −1.21872 | ||||||||
\(626\) | −86.0505 | −3.43927 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −91.2954 | −3.64308 | ||||||||
\(629\) | 19.3074 | 0.769837 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.9311 | 1.51001 | 0.755007 | − | 0.655717i | \(-0.227634\pi\) | ||||
0.755007 | + | 0.655717i | \(0.227634\pi\) | |||||||
\(632\) | −78.3781 | −3.11771 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.7723 | 0.427823 | ||||||||
\(635\) | 4.93454 | 0.195821 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.7194 | −1.05866 | ||||||||
\(638\) | −14.2884 | −0.565684 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 42.8928 | 1.69549 | ||||||||
\(641\) | −18.8879 | −0.746028 | −0.373014 | − | 0.927826i | \(-0.621676\pi\) | ||||
−0.373014 | + | 0.927826i | \(0.621676\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.97232 | −0.235525 | −0.117763 | − | 0.993042i | \(-0.537572\pi\) | ||||
−0.117763 | + | 0.993042i | \(0.537572\pi\) | |||||||
\(644\) | −1.37516 | −0.0541891 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.0522 | −1.53649 | ||||||||
\(647\) | 11.1527 | 0.438458 | 0.219229 | − | 0.975673i | \(-0.429646\pi\) | ||||
0.219229 | + | 0.975673i | \(0.429646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.7821 | 1.95412 | ||||||||
\(650\) | 34.8429 | 1.36665 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 63.4530 | 2.48501 | ||||||||
\(653\) | 37.7960 | 1.47907 | 0.739536 | − | 0.673117i | \(-0.235045\pi\) | ||||
0.739536 | + | 0.673117i | \(0.235045\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.2960 | −1.14469 | ||||||||
\(656\) | 31.5908 | 1.23341 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.76101 | −0.341540 | ||||||||
\(659\) | −42.4555 | −1.65383 | −0.826915 | − | 0.562327i | \(-0.809906\pi\) | ||||
−0.826915 | + | 0.562327i | \(0.809906\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.4778 | 1.14655 | 0.573276 | − | 0.819362i | \(-0.305672\pi\) | ||||
0.573276 | + | 0.819362i | \(0.305672\pi\) | |||||||
\(662\) | 45.9882 | 1.78738 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41.2148 | −1.59945 | ||||||||
\(665\) | 3.32970 | 0.129120 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 35.2734 | 1.36477 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −42.1534 | −1.62853 | ||||||||
\(671\) | −50.2754 | −1.94086 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.5427 | 1.10024 | 0.550121 | − | 0.835085i | \(-0.314582\pi\) | ||||
0.550121 | + | 0.835085i | \(0.314582\pi\) | |||||||
\(674\) | −15.1371 | −0.583058 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.60763 | 0.369524 | ||||||||
\(677\) | −13.7924 | −0.530083 | −0.265042 | − | 0.964237i | \(-0.585386\pi\) | ||||
−0.265042 | + | 0.964237i | \(0.585386\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.951344 | 0.0365092 | ||||||||
\(680\) | 82.4699 | 3.16258 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −43.7242 | −1.67428 | ||||||||
\(683\) | −1.11404 | −0.0426275 | −0.0213137 | − | 0.999773i | \(-0.506785\pi\) | ||||
−0.0213137 | + | 0.999773i | \(0.506785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.68296 | −0.331759 | ||||||||
\(686\) | 9.97386 | 0.380804 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −74.6167 | −2.84473 | ||||||||
\(689\) | 48.4228 | 1.84476 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6753 | −0.482190 | −0.241095 | − | 0.970502i | \(-0.577507\pi\) | ||||
−0.241095 | + | 0.970502i | \(0.577507\pi\) | |||||||
\(692\) | 31.9125 | 1.21313 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.2766 | −1.14929 | ||||||||
\(695\) | −34.3229 | −1.30194 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.96285 | 0.339492 | ||||||||
\(698\) | −81.1243 | −3.07060 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.65388 | −0.175900 | ||||||||
\(701\) | −9.37223 | −0.353984 | −0.176992 | − | 0.984212i | \(-0.556637\pi\) | ||||
−0.176992 | + | 0.984212i | \(0.556637\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.2543 | −0.914770 | ||||||||
\(704\) | −91.5187 | −3.44924 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −86.1292 | −3.24151 | ||||||||
\(707\) | 0.395290 | 0.0148664 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −47.9902 | −1.80231 | −0.901155 | − | 0.433496i | \(-0.857280\pi\) | ||||
−0.901155 | + | 0.433496i | \(0.857280\pi\) | |||||||
\(710\) | 108.664 | 4.07808 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −52.2633 | −1.95865 | ||||||||
\(713\) | 3.06011 | 0.114602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −59.7716 | −2.23533 | ||||||||
\(716\) | −115.086 | −4.30095 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.44585 | −0.203237 | ||||||||
\(719\) | −12.9071 | −0.481354 | −0.240677 | − | 0.970605i | \(-0.577369\pi\) | ||||
−0.240677 | + | 0.970605i | \(0.577369\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.29736 | 0.160042 | ||||||||
\(722\) | −1.66321 | −0.0618983 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −21.9974 | −0.817529 | ||||||||
\(725\) | 3.38424 | 0.125687 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.6458 | 0.876975 | 0.438487 | − | 0.898737i | \(-0.355514\pi\) | ||||
0.438487 | + | 0.898737i | \(0.355514\pi\) | |||||||
\(728\) | −8.63463 | −0.320021 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −48.5207 | −1.79583 | ||||||||
\(731\) | −21.1700 | −0.783002 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.0760 | 0.446036 | 0.223018 | − | 0.974814i | \(-0.428409\pi\) | ||||
0.223018 | + | 0.974814i | \(0.428409\pi\) | |||||||
\(734\) | −67.0168 | −2.47363 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15.4162 | 0.568249 | ||||||||
\(737\) | 29.1884 | 1.07517 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.6117 | −0.647858 | −0.323929 | − | 0.946081i | \(-0.605004\pi\) | ||||
−0.323929 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(740\) | 83.9853 | 3.08736 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.99099 | −0.330070 | ||||||||
\(743\) | −19.7219 | −0.723528 | −0.361764 | − | 0.932270i | \(-0.617825\pi\) | ||||
−0.361764 | + | 0.932270i | \(0.617825\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.08746 | 0.149753 | ||||||||
\(746\) | 61.3933 | 2.24777 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −93.6348 | −3.42363 | ||||||||
\(749\) | −4.47042 | −0.163345 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.4318 | −1.18345 | −0.591726 | − | 0.806139i | \(-0.701553\pi\) | ||||
−0.591726 | + | 0.806139i | \(0.701553\pi\) | |||||||
\(752\) | 147.152 | 5.36609 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.2956 | 0.374945 | ||||||||
\(755\) | 12.0547 | 0.438717 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.32070 | −0.120693 | −0.0603464 | − | 0.998177i | \(-0.519221\pi\) | ||||
−0.0603464 | + | 0.998177i | \(0.519221\pi\) | |||||||
\(758\) | 79.8796 | 2.90136 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −103.600 | −3.75798 | ||||||||
\(761\) | 0.490170 | 0.0177687 | 0.00888433 | − | 0.999961i | \(-0.497172\pi\) | ||||
0.00888433 | + | 0.999961i | \(0.497172\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.73108 | 0.135074 | ||||||||
\(764\) | −85.7955 | −3.10397 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57.5273 | 2.07855 | ||||||||
\(767\) | −35.8709 | −1.29522 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.0431 | −1.48005 | −0.740026 | − | 0.672578i | \(-0.765187\pi\) | ||||
−0.740026 | + | 0.672578i | \(0.765187\pi\) | |||||||
\(770\) | 11.0982 | 0.399951 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 83.5357 | 3.00652 | ||||||||
\(773\) | 19.0840 | 0.686405 | 0.343202 | − | 0.939261i | \(-0.388488\pi\) | ||||
0.343202 | + | 0.939261i | \(0.388488\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3561 | 0.372003 | ||||||||
\(776\) | −29.6002 | −1.06258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 48.1986 | 1.72800 | ||||||||
\(779\) | −11.2593 | −0.403407 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.2425 | −2.69239 | ||||||||
\(782\) | 9.10980 | 0.325766 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −83.3291 | −2.97604 | ||||||||
\(785\) | −51.5658 | −1.84046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4980 | −0.588091 | −0.294045 | − | 0.955791i | \(-0.595002\pi\) | ||||
−0.294045 | + | 0.955791i | \(0.595002\pi\) | |||||||
\(788\) | −105.761 | −3.76759 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −72.5891 | −2.58261 | ||||||||
\(791\) | −0.0656398 | −0.00233388 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 36.2263 | 1.28643 | ||||||||
\(794\) | −1.12470 | −0.0399142 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −65.7963 | −2.33209 | ||||||||
\(797\) | 17.4840 | 0.619314 | 0.309657 | − | 0.950848i | \(-0.399786\pi\) | ||||
0.309657 | + | 0.950848i | \(0.399786\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 41.7496 | 1.47700 | ||||||||
\(800\) | 52.1721 | 1.84456 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 81.0839 | 2.86317 | ||||||||
\(803\) | 33.5974 | 1.18563 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.776726 | −0.0273760 | ||||||||
\(806\) | 31.5058 | 1.10974 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.2991 | −0.432679 | ||||||||
\(809\) | −41.6731 | −1.46515 | −0.732575 | − | 0.680687i | \(-0.761682\pi\) | ||||
−0.732575 | + | 0.680687i | \(0.761682\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.9138 | 0.664153 | 0.332076 | − | 0.943253i | \(-0.392251\pi\) | ||||
0.332076 | + | 0.943253i | \(0.392251\pi\) | |||||||
\(812\) | −1.37516 | −0.0482588 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −80.8420 | −2.83351 | ||||||||
\(815\) | 35.8398 | 1.25541 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.5942 | 0.930413 | ||||||||
\(818\) | 62.9041 | 2.19939 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 38.9875 | 1.36150 | ||||||||
\(821\) | 17.6801 | 0.617039 | 0.308520 | − | 0.951218i | \(-0.400166\pi\) | ||||
0.308520 | + | 0.951218i | \(0.400166\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.9917 | 1.15002 | 0.575010 | − | 0.818147i | \(-0.304998\pi\) | ||||
0.575010 | + | 0.818147i | \(0.304998\pi\) | |||||||
\(824\) | −133.708 | −4.65795 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.66039 | 0.231745 | ||||||||
\(827\) | −3.30724 | −0.115004 | −0.0575020 | − | 0.998345i | \(-0.518314\pi\) | ||||
−0.0575020 | + | 0.998345i | \(0.518314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 49.4697 | 1.71815 | 0.859077 | − | 0.511847i | \(-0.171039\pi\) | ||||
0.859077 | + | 0.511847i | \(0.171039\pi\) | |||||||
\(830\) | −38.1707 | −1.32493 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 65.9445 | 2.28621 | ||||||||
\(833\) | −23.6419 | −0.819143 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.9233 | 0.689473 | ||||||||
\(836\) | 117.626 | 4.06818 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 85.1824 | 2.94258 | ||||||||
\(839\) | 32.6645 | 1.12771 | 0.563853 | − | 0.825875i | \(-0.309319\pi\) | ||||
0.563853 | + | 0.825875i | \(0.309319\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −52.5239 | −1.81009 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 48.1729 | 1.65818 | ||||||||
\(845\) | 5.42662 | 0.186681 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.73403 | −0.162663 | ||||||||
\(848\) | 151.015 | 5.18588 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.8297 | 1.05745 | ||||||||
\(851\) | 5.65787 | 0.193949 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.7627 | −0.882098 | −0.441049 | − | 0.897483i | \(-0.645393\pi\) | ||||
−0.441049 | + | 0.897483i | \(0.645393\pi\) | |||||||
\(854\) | −6.72638 | −0.230172 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 139.093 | 4.75409 | ||||||||
\(857\) | −35.2332 | −1.20354 | −0.601771 | − | 0.798669i | \(-0.705538\pi\) | ||||
−0.601771 | + | 0.798669i | \(0.705538\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.7520 | 1.04924 | 0.524622 | − | 0.851335i | \(-0.324207\pi\) | ||||
0.524622 | + | 0.851335i | \(0.324207\pi\) | |||||||
\(860\) | −92.0875 | −3.14016 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −92.3975 | −3.14707 | ||||||||
\(863\) | −49.9199 | −1.69929 | −0.849647 | − | 0.527352i | \(-0.823185\pi\) | ||||
−0.849647 | + | 0.527352i | \(0.823185\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0249 | 0.612866 | ||||||||
\(866\) | 72.9929 | 2.48040 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.20815 | −0.142834 | ||||||||
\(869\) | 50.2631 | 1.70506 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.0319 | −0.712640 | ||||||||
\(872\) | −116.089 | −3.93127 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.4439 | −0.387096 | ||||||||
\(875\) | 1.25500 | 0.0424269 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.83191 | 0.230697 | 0.115349 | − | 0.993325i | \(-0.463202\pi\) | ||||
0.115349 | + | 0.993325i | \(0.463202\pi\) | |||||||
\(878\) | 69.4569 | 2.34406 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −186.408 | −6.28382 | ||||||||
\(881\) | −32.6335 | −1.09945 | −0.549725 | − | 0.835346i | \(-0.685268\pi\) | ||||
−0.549725 | + | 0.835346i | \(0.685268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.6050 | 1.33282 | 0.666408 | − | 0.745587i | \(-0.267831\pi\) | ||||
0.666408 | + | 0.745587i | \(0.267831\pi\) | |||||||
\(884\) | 67.4692 | 2.26924 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.0800 | 0.674600 | ||||||||
\(887\) | −22.2862 | −0.748297 | −0.374148 | − | 0.927369i | \(-0.622065\pi\) | ||||
−0.374148 | + | 0.927369i | \(0.622065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.457142 | −0.0153320 | ||||||||
\(890\) | −48.4032 | −1.62248 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −111.632 | −3.73773 | ||||||||
\(893\) | −52.4467 | −1.75506 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −65.0031 | −2.17281 | ||||||||
\(896\) | −3.97364 | −0.132750 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −110.199 | −3.67740 | ||||||||
\(899\) | 3.06011 | 0.102060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 42.8456 | 1.42739 | ||||||||
\(902\) | −37.5283 | −1.24956 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.04232 | 0.0679265 | ||||||||
\(905\) | −12.4247 | −0.413010 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.7700 | 1.08811 | 0.544054 | − | 0.839050i | \(-0.316888\pi\) | ||||
0.544054 | + | 0.839050i | \(0.316888\pi\) | |||||||
\(908\) | −54.6657 | −1.81415 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.99688 | −0.265094 | ||||||||
\(911\) | 29.1155 | 0.964640 | 0.482320 | − | 0.875995i | \(-0.339794\pi\) | ||||
0.482320 | + | 0.875995i | \(0.339794\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.4307 | 0.874728 | ||||||||
\(914\) | 50.7093 | 1.67732 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 49.6592 | 1.64079 | ||||||||
\(917\) | 2.71401 | 0.0896246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.2277 | −0.865173 | −0.432586 | − | 0.901592i | \(-0.642399\pi\) | ||||
−0.432586 | + | 0.901592i | \(0.642399\pi\) | |||||||
\(920\) | 24.1671 | 0.796765 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 63.5216 | 2.09197 | ||||||||
\(923\) | 54.2165 | 1.78456 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19.1476 | 0.629568 | ||||||||
\(926\) | −6.48786 | −0.213204 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 15.4162 | 0.506062 | ||||||||
\(929\) | 49.4635 | 1.62285 | 0.811423 | − | 0.584459i | \(-0.198693\pi\) | ||||
0.811423 | + | 0.584459i | \(0.198693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 29.6994 | 0.973358 | ||||||||
\(932\) | −91.8602 | −3.00898 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.3077 | 0.599046 | ||||||||
\(935\) | −52.8872 | −1.72960 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.95297 | 0.129138 | 0.0645690 | − | 0.997913i | \(-0.479433\pi\) | ||||
0.0645690 | + | 0.997913i | \(0.479433\pi\) | |||||||
\(938\) | 3.90514 | 0.127507 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 181.607 | 5.92336 | ||||||||
\(941\) | 18.6695 | 0.608607 | 0.304304 | − | 0.952575i | \(-0.401576\pi\) | ||||
0.304304 | + | 0.952575i | \(0.401576\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.62648 | 0.0855301 | ||||||||
\(944\) | −111.870 | −3.64105 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 88.6410 | 2.88197 | ||||||||
\(947\) | −15.3063 | −0.497389 | −0.248694 | − | 0.968582i | \(-0.580001\pi\) | ||||
−0.248694 | + | 0.968582i | \(0.580001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.2088 | −0.785852 | ||||||||
\(950\) | −38.7289 | −1.25653 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −7.64011 | −0.247617 | ||||||||
\(953\) | −24.5884 | −0.796498 | −0.398249 | − | 0.917277i | \(-0.630382\pi\) | ||||
−0.398249 | + | 0.917277i | \(0.630382\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.4593 | −1.56811 | ||||||||
\(956\) | 7.85997 | 0.254210 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −43.7609 | −1.41385 | ||||||||
\(959\) | 0.804399 | 0.0259754 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6357 | −0.697927 | ||||||||
\(962\) | 58.2513 | 1.87810 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.6478 | 0.987100 | ||||||||
\(965\) | 47.1829 | 1.51887 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.3203 | 0.878561 | 0.439281 | − | 0.898350i | \(-0.355233\pi\) | ||||
0.439281 | + | 0.898350i | \(0.355233\pi\) | |||||||
\(968\) | 147.295 | 4.73424 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −27.4139 | −0.880208 | ||||||||
\(971\) | 34.6915 | 1.11330 | 0.556652 | − | 0.830746i | \(-0.312086\pi\) | ||||
0.556652 | + | 0.830746i | \(0.312086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.17971 | 0.101937 | ||||||||
\(974\) | −84.0043 | −2.69167 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 112.978 | 3.61634 | ||||||||
\(977\) | 33.7185 | 1.07875 | 0.539375 | − | 0.842065i | \(-0.318660\pi\) | ||||
0.539375 | + | 0.842065i | \(0.318660\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.5160 | 1.07118 | ||||||||
\(980\) | −102.840 | −3.28510 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 91.0024 | 2.90400 | ||||||||
\(983\) | 21.7136 | 0.692556 | 0.346278 | − | 0.938132i | \(-0.387445\pi\) | ||||
0.346278 | + | 0.938132i | \(0.387445\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −59.7365 | −1.90336 | ||||||||
\(986\) | 9.10980 | 0.290115 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −84.7562 | −2.69645 | ||||||||
\(989\) | −6.20369 | −0.197266 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.8122 | −0.756418 | −0.378209 | − | 0.925720i | \(-0.623460\pi\) | ||||
−0.378209 | + | 0.925720i | \(0.623460\pi\) | |||||||
\(992\) | 47.1753 | 1.49782 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.0668 | −0.319298 | ||||||||
\(995\) | −37.1633 | −1.17816 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −42.4682 | −1.34498 | −0.672490 | − | 0.740106i | \(-0.734775\pi\) | ||||
−0.672490 | + | 0.740106i | \(0.734775\pi\) | |||||||
\(998\) | 61.9232 | 1.96015 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.n.1.12 | 12 | ||
3.2 | odd | 2 | 667.2.a.b.1.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
667.2.a.b.1.1 | ✓ | 12 | 3.2 | odd | 2 | ||
6003.2.a.n.1.12 | 12 | 1.1 | even | 1 | trivial |